Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-05-22
Phys.Rev. D54 (1996) 7338-7352
Physics
High Energy Physics
High Energy Physics - Theory
28 pages, LaTeX, 1 Postscript figure, uses epsf.sty
Scientific paper
10.1103/PhysRevD.54.7338
We analyze the stability properties of the purely magnetic, static solutions to the Einstein--Yang--Mills equations with cosmological constant. It is shown that all three classes of solutions found in a recent study are unstable under spherical perturbations. Specifically, we argue that the configurations have $n$ unstable modes in each parity sector, where $n$ is the number of nodes of the magnetic Yang--Mills amplitude of the background solution. The ``sphaleron--like'' instabilities (odd parity modes) decouple from the gravitational perturbations. They are obtained from a regular Schr\"odinger equation after a supersymmetric transformation. The body of the work is devoted to the fluctuations with even parity. The main difficulty arises because the Schwarzschild gauge -- which is usually imposed to eliminate the gravitational perturbations from the Yang--Mills equation -- is not regular for solutions with compact spatial topology. In order to overcome this problem, we derive a gauge invariant formalism by virtue of which the unphysical (gauge) modes can be isolated.
Brodbeck Othmar
Heusler Markus
Straumann Lavrelashvili G. N.
Volkov Mikhail S.
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